Download PDF by G. W. Stewart: Afternotes on numerical analysis: a series of lectures on

By G. W. Stewart

ISBN-10: 0898713625

ISBN-13: 9780898713626

This is often an outstanding straightforward creation to numerical research, in basic terms simple arithmetic is needed. it really is enjoyable and simple to learn. this can be a "small" booklet; the biggest part (linear equations) being sixty six pages. although, it does disguise loads of ground.

Code fragments are in C and FORTRAN. The C code evidently hasn't been demonstrated (abs() rather than fabs() throughout). there are lots of typos within the textual content in addition to within the code fragments.

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Extra resources for Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the University of Maryland at College Park and recorded after the fact

Example text

In outline, the iteration proceeds as follows. The input is three points Xk, #fc-i, £/c-2> and the corresponding function values. 1. Find a quadratic polynomial g ( x ) such that g(xi) = /(#j), (i = k. k — l,fc-2). 2. 2. A horrible example. It is a worthwhile exercise to work out the details. 20. Muller's method has the advantage that it can produce complex iterates from real starting values. This feature is not shared by either Newton's method or the secant method. The linear-fractional method 21.

At x* to determine if x* is an attractive fixed point. We will skip the slightly tedious differentiation and get straight to the result: Therefore, Newton's method converges to a multiple zero from any sufficiently close approximation, and the convergence is linear with ratio 1 — —. tn In particular for a double root, the ratio is ^, which is comparable with the convergence of interval bisection. 3. Nonlinear Equations 25 Ending with a proposition 20. Although roots that are exactly multiple are not common in practice, the above theory says something about how Newton's method behaves with a nearly multiple root.

The reasoning is as follows. The old value of b has a different sign than the old value of c. The new value of b has the same sign as the old value of c. Consequently, the replacement results in a new value of c that has a different sign than the new value of b. In making the substitution, it is important to remember that the old value of b is now contained in a. 1. A problem with c. if (sign(fb) == sign(fc)){ c = a; fc = fa; } 14. 2). 15. Finally, we return after leaving the while loop. } return; 16.

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Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the University of Maryland at College Park and recorded after the fact by G. W. Stewart


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